The figure shows how the distribution of a sampling proportion appears when the sample size is n=10

Question

, n=100
, and n=1000
. How does the range of variability and the shape of the distribution change as the sample size becomes larger?

(1 point)
Responses

As the sample size increases, the range of variability decreases, and the shape of the distribution becomes more symmetric.
As the sample size increases, the range of variability decreases, and the shape of the distribution becomes more symmetric.

As the sample size increases, the range of variability increases, and the shape of the distribution becomes more symmetric.
As the sample size increases, the range of variability increases, and the shape of the distribution becomes more symmetric.
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Answer 1

As the sample size increases, the correct response is:

"As the sample size increases, the range of variability decreases, and the shape of the distribution becomes more symmetric."

This is consistent with the Central Limit Theorem, which states that as the sample size grows, the sampling distribution of the sample proportion approaches a normal distribution, regardless of the shape of the population distribution. Additionally, larger sample sizes reduce variability (or standard error) in the sampling proportions, leading to a more concentrated distribution around the true population proportion.